The classically conformal B-L extended standard model

Yuta Orikasa

Satoshi Iso(KEK,SOKENDAI)Nobuchika Okada(University of Alabama)Phys.Lett.B676(2009)81Phys.Rev.D80(2009)115007Phys.Rev.D83(2011)093011

Classically conformal SMWe assume the classically conformal invariance.This invariance forbids the Higgs mass term. Therefore there is no electroweak symmetry breaking at the classical level.We need to consider origin of the symmetry breaking.

Coleman-Weinberg Mechanism(radiative symmetry

breaking)Calculate quantum correction

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In the classically conformal SM, due to the large top mass the effective potential is rendered unstable, and CW mechanism does not work.

However, top quark is heavy, so the stability condition does not satisfy.

The effective potential is not stabilized.

We need to extend SM. We propose classically conformal minimal B-L extended model.

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Contents

•Introduction•Classically conformal B-L extended Standard Model

•Phenomenological bound•Collider physics•Thermal leptogenesis•Neutrino oscillation data and resonant leptogenesis

•Conclusion

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Classically conformal B-L extended Standard Model

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Classically conformal B-L extended Model

Gauge symmetry

New particles　 right-handed neutrino　 SM singlet scalar　　　 gauge field

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LagrangianWe assume classically conformal invariance

Yukawa sector

Dirac Yukawa

Majorana Yukawa

See-Saw mechanism associates with B-L symmetry breaking.

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Potential

at planck scale

Renormalization group equations for masses

Classically conformal invariance

Potential

at planck scale

Renormalization group equations for masses

Classically conformal invariance

Potential

at planck scale

Assumption

Renormalization group equations for quartic couplings

is very small and negative

In our model, if majorana Yukawa coupling is small, the stability condition satisfies.

The potential has non-trivial minimum.

B-L symmetry is broken by CW mechanism.

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Electroweak symmetry breaking

Effective tree-level mass squared is induced.EW symmetry breaking occurs as usual in the SM.

Once the B-L symmetry is broken, the SM Higgs doublet mass is generated through the mixing term between H and Φ in the scalar potential.

Φ has VEV M.

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TeV scale B-L model

If the B-L gauge coupling and the SM gauge couplings are same order, B-L breaking scale is around a few TeV.

Phenomenological bound

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LEP bound

LEP experiments provided a severe constraint.

LEP bound

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Collider physics

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Z’ boson at LHC We calculate the dilepton production cross section through the Z’ boson exchange together with the SM processes mediated by Z boson and photon.

SM background

Z’ exchange

A clear peak of Z’ resonance

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Z’ boson at ILC(International Linear Collider)

We calculate the cross section of the process → 　　 at the ILC with a collider energy =1 TeV.

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Excluded by LEP LHC

reach

ILC reach

The figure indicates that if the B-L gauge coupling is not much smaller than the SM gauge couplings, Z’ boson mass is around a few TeV.

Thermal leptogenesis

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Leptogenesis

ε=0.01

Initial condition

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Wash out for inverse decay

suppressed by Z’ exchange process

CP Asymmetry

Vertex contribution

Self-energy contribution

Right-handed Majorana neutrino can decay into lepton and anti-lepton.

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Majorana mass bound

The Majorana mass is heavier than .

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If right-handed neutrinos have a hierarchical mass spectrum 　 ,we can write a CP asymmetry as

Baryon asymmetry is

Resonant Leptogenesis

•The Majorana mass is heavier than ,if the spectrum of Majorana masses has hierarchy.

•If the Majorana mass of right-handed neutrino is smaller than a few TeV, general leptogenesis can not work.

Resonant-Leptogenesis

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resonant-leptogenesis

If two right-handed neutrinos have mass differences comparable to their decay widths , self-energy correction dominate.

can be even .

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Neutrino oscillation data and resonant leptogenesis

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More realistic case

Neutrino oscillation data(2σ)

Any model of leptogenesis should reproduce these masses and mixing angles.

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Assumptions

Assumption ⅡNeutrino mixing matrix is tri-bimaximal matrix, when CP phase is zero.

Assumption Ⅰ 　Only two right-handed neutrino are relevant to neutrino oscillation. Dirac Yukawa matrix is 2×3 matrix.

Assumption ⅢHierarchal neutrino mass spectrum.

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Baryon asymmetry in our universe

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Mass difference

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Mixing angle31

Conclusion

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Conclusions•We propose the classically conformal minimal B-

L model.

•B-L symmetry and EW symmetry are broken by CW mechanism.

•Our model naturally predicts B-L breaking scale at TeV. Z’ boson can be discovered in the near future.

•Based on assumptions, we analyze neutrino oscillation data and B as a function of a single CP phase. We have found a fixed CP phase can reproduce both all neutrino oscillation data and observed baryon asymmetry.

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Theoretical boundThe bound of B-L gauge coupling

We impose the condition that B-L gauge coupling does not blow up to Planck scale.

For TeV scale B-L symmetry breaking, we find

αB-L

scale

Planck scale

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We consider minimal flavor violation

Flavor symmetry violates the effect of Dirac Yukawa coupling

Resonant leptogenesis

At high energy scale, the Majorana masses have same value

Quantum correction for the Majorana masses